History
The twelfth root of two was calculated accurately by the Chinese court astronomer, historian, physicist and mathematician Zhu Zaiyu, Prince of Zheng of the Ming Dynasty. In 1584, Zhu published a work 律呂精義 A clear explanation of that which concerns the 律 . Prince Zhu made note of the difference between his ideal mathematically-tuned 呂 (ancient music instrument), which gave the theoretical music instrument lengths for 12-tone equal temperament correct to 25 places, implemented with an 81-column abacus and calculated the cubic root of the square root of the square root of 2, obtaining which coincidentally applied a form of Pythagorean tuning.
Calculated again in 1636 by the French mathematician Marin Mersenne, and as the techniques for calculating logarithms develop, the original approach for calculation would eventually become trivial.
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